Problem: Simplify the following expression: $ z = \dfrac{-8p}{4p + 5} + 3 $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the second expression by $\dfrac{4p + 5}{4p + 5}$ $ \dfrac{-3}{1} \times \dfrac{4p + 5}{4p + 5} = \dfrac{-12p - 15}{4p + 5} $ Therefore $ z = \dfrac{-8p}{4p + 5} - \dfrac{-12p - 15}{4p + 5} $ Now the expressions have the same denominator we can simply subtract the numerators: $z = \dfrac{-8p - (-12p - 15) }{4p + 5} $ Distribute the negative sign: $z = \dfrac{-8p + 12p + 15}{4p + 5}$ $z = \dfrac{4p + 15}{4p + 5}$